Modeling Melt Spinning with Stress Induced Crystallization at High Take Up Velocities: Numerical Results for the PET Melt

Abstract

The purpose of this work is to present a 2-D thermo-rheological model for high take up velocities that can predict numerically in the filament domain, the axial velocity profile together with the radial and axial resolutions of stresses, temperature and degree of crystallization. The rheology of the filament is described through a constitutive equation that results from the combination of the Phan-Thien and Tanner viscoelastic model for the amorphous phase and the kinetic model of the rigid dumbbell for the crystalline phase immersed in the melt. The model is thus able to predict the thermal and mechanical coupling between both phases through the degree of transformation (relative degree of crystallization) when the balances of mass, momentum and energy are invoked. The effects of stress induced crystallization, viscoelasticity, friction of cooling air, filament inertia, gravity and surface tension are all considered together with the temperature dependency of polymer and cooling air thermo-physical properties. The rate of crystallization is evaluated through the nonisothermal Avrami-Nakamura equation. Also, the relaxation times of both phases are function of temperature and degree of transformation. Numerical predictions of the model compare well with experimental data reported in the literature for a PET melt at a take up velocity of 5490 m/min. Also, consistently with experimental observations reported in the literature, the “skin-core” structure is predicted. It is relevant to indicate that the model analyzed here can be evaluated from low to high take up velocities, and when the degree of crystallization becomes negligible, the one-phase model is recovered continuously.